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The Annals of Applied Probability publishes research papers of
the highest quality reflecting the many facets of contemporary applied probability.
Primary emphasis is placed on importance and originality.The Annals of Applied Probability has two over-riding criteria
for publishing of papers, other than formal correctness and coherence. These
are:
(a) that the results in the paper should be genuinely applied or applicable;
and
(b) that the paper should make a serious contribution to the mathematical
theory of probability, or in some other sense carry a substantial level of
probabilistic innovation, or be likely to stimulate such innovation.
Fundamentally, we seek a broad spectrum of papers which intellectually
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thinking has a role in solving real applied problems, interpreted in a wide
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Abstract

We study the class of tree-growing search strategies introduced by Lent and Mahmoud, searches for which data are stored in a deterministic sequence of tree structures (e.g., linear search in forward order). Specifically, we study the conditions under which the number of comparisons needed to sort a sequence of randomly ordered numbers is asymptotically normal. Our main result is a sufficient condition for normality in terms of the growth rate of tree height alone; this condition is easily computed and is satisfied by all standard deterministic search strategies. We also give some examples of normal search strategies with surprisingly small variance, in particular, much smaller than is possible for the class of consistent strategies that are the focus of the work by Lent and Mahmoud.